| CODE | IFS0014 | ||||||||||||
| TITLE | Calculus and Numerical Methods | ||||||||||||
| UM LEVEL | 00 - Mod Pre-Tert, Foundation, Proficiency & DegreePlus | ||||||||||||
| MQF LEVEL | 4 | ||||||||||||
| ECTS CREDITS | 5 | ||||||||||||
| DEPARTMENT | Engineering and ICT | ||||||||||||
| DESCRIPTION | This study-unit introduces mathematical concepts to provide an introduction to calculus through the study of differentiation and integration. The students will be given the opportunity to apply differentiation and integration to solve simple problems on maxima and minima, rate of change, areas, volumes and length of arcs, and to solve first order and second order differential equations. Numerical methods to find approximate values of roots of equations, of series, and of definite integrals will be also explored and implemented. Study-unit Aims: To provide: - A review of the gradient of a line and curve, of the equations of tangents and normals, and of simple curve sketching; - An introductory overview to limits, differentiation, integration and differential equations; - An outline of the applications of differentiation and integration to solving differential equations and other problems arising from real-life situations; - An outline of the applications of numerical methods to find valid approximations. Learning Outcomes: 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: - Describe the derivative as a limit; - Identify problems on rate of change, maxima and minima- View integration as a process of summation and as the inverse of differentiation; - Distinguish between first order and second order differential equations; - Explain the use of the trapezium rule and of Simpson's rule and appreciate the use of numerical techniques to obtain an approximate but useful solution. 2. Skills: By the end of the study-unit the student will be able to: - Differentiate algebraic, exponential, logarithmic, trigonometric hyperbolic and their inverses, implicit and parametric functions; - Differentiate sums, products, quotients and composition of functions; - Apply differentiation to gradients, tangents and normals, and to simple problems involving rates of change, maxima and minima; - Use trigonometric identities to integrate functions; - Evaluate integrals by means of standard forms, by substitution, by partial fractions and by parts; - Apply integration to calculate areas and mean values of functions; - Calculate volume of revolution, arc length and area of surface of revolution using Cartesian or parametric coordinates; - Solve first order differential equations (separable variables and linear) and second order differential equations (with constant coefficients); - Locate the roots of an equation by considering changes of sign and find an approximation to such root by the Newton-Raphson method; - Use the trapezium rule and Simpson’s rule as approximations in definite integration. Main Text/s and any supplementary readings: - L. Bostock and S. Chandler (2014). Mathematics The Core Course for A-Level. Stanley Thornes. ISBN: 9780859503068. - L. Bostock, S. Chandler and C. Rourke (1982). Further Pure Mathematics. Stanley Thornes. ISBN: 9780859501033. |
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| ADDITIONAL NOTES | Please note that a pass in the Examination component is obligatory for an overall pass mark to be awarded. | ||||||||||||
| STUDY-UNIT TYPE | Lecture, Independent Study & Tutorial | ||||||||||||
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The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints. Units not attracting a sufficient number of registrations may be withdrawn without notice. It should be noted that all the information in the description above applies to study-units available during the academic year 2024/5. It may be subject to change in subsequent years. |
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